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Given the function at h (x) =x²-7x+6
(1) Express h(a²) -g(a) in terms of a
(2) find the value of k for which h (k)=0
(3) Express h (2a) -h (a+1) interms of a?
(1) Express h(a²) -g(a) in terms of a
(2) find the value of k for which h (k)=0
(3) Express h (2a) -h (a+1) interms of a?
Most Upvoted Answer
Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms o...
Expressing h(a²) - g(a) in terms of a:
- Substituting a² into the function h(x) = x² - 7x + 6, we get h(a²) = (a²)² - 7(a²) + 6 = a⁴ - 7a² + 6
- Substituting a into the function g(x) = 2x - 3, we get g(a) = 2a - 3
- Therefore, h(a²) - g(a) = (a⁴ - 7a² + 6) - (2a - 3) = a⁴ - 7a² + 6 - 2a + 3 = a⁴ - 7a² - 2a + 9
Finding the value of k for which h(k) = 0:
- Setting h(k) = k² - 7k + 6 to 0, we get k² - 7k + 6 = 0
- Factoring the quadratic equation, we get (k - 6)(k - 1) = 0
- Therefore, k = 6 or k = 1
Expressing h(2a) - h(a+1) in terms of a:
- Substituting 2a into the function h(x) = x² - 7x + 6, we get h(2a) = (2a)² - 7(2a) + 6 = 4a² - 14a + 6
- Substituting (a+1) into the function h(x), we get h(a+1) = (a+1)² - 7(a+1) + 6 = a² + 2a + 1 - 7a - 7 + 6 = a² - 5a
- Therefore, h(2a) - h(a+1) = (4a² - 14a + 6) - (a² - 5a) = 4a² - 14a + 6 - a² + 5a = 3a² - 9a + 6
- Substituting a² into the function h(x) = x² - 7x + 6, we get h(a²) = (a²)² - 7(a²) + 6 = a⁴ - 7a² + 6
- Substituting a into the function g(x) = 2x - 3, we get g(a) = 2a - 3
- Therefore, h(a²) - g(a) = (a⁴ - 7a² + 6) - (2a - 3) = a⁴ - 7a² + 6 - 2a + 3 = a⁴ - 7a² - 2a + 9
Finding the value of k for which h(k) = 0:
- Setting h(k) = k² - 7k + 6 to 0, we get k² - 7k + 6 = 0
- Factoring the quadratic equation, we get (k - 6)(k - 1) = 0
- Therefore, k = 6 or k = 1
Expressing h(2a) - h(a+1) in terms of a:
- Substituting 2a into the function h(x) = x² - 7x + 6, we get h(2a) = (2a)² - 7(2a) + 6 = 4a² - 14a + 6
- Substituting (a+1) into the function h(x), we get h(a+1) = (a+1)² - 7(a+1) + 6 = a² + 2a + 1 - 7a - 7 + 6 = a² - 5a
- Therefore, h(2a) - h(a+1) = (4a² - 14a + 6) - (a² - 5a) = 4a² - 14a + 6 - a² + 5a = 3a² - 9a + 6
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Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a?
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Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a?.
Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the function at h (x) =x²-7x+6(1) Express h(a²) -g(a) in terms of a (2) find the value of k for which h (k)=0(3) Express h (2a) -h (a+1) interms of a?.
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