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If f: R → R and g: R → R defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the value of x for which f(g(x)) = 25 is
- a)±3
- b)±1
- c)±4
- d)±2
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If f: R → R and g: R → R defined by f(x) = 2x + 3 andg(x) ...
To find the value of x for which f(g(x)) = 25, we need to substitute g(x) into the function f(x) and solve for x.
Given:
f(x) = 2x - 3
g(x) = x^2 - 7
Substituting g(x) into f(x), we have:
f(g(x)) = 2(g(x)) - 3
= 2(x^2 - 7) - 3
= 2x^2 - 14 - 3
= 2x^2 - 17
Now we can set this expression equal to 25 and solve for x:
2x^2 - 17 = 25
Adding 17 to both sides:
2x^2 = 42
Dividing both sides by 2:
x^2 = 21
Taking the square root of both sides:
x = ±√21
Since we are looking for a real value of x, we can discard the negative square root.
Therefore, the value of x for which f(g(x)) = 25 is x = √21, which is approximately 4.58.
So, the correct answer is option D) 2.
Given:
f(x) = 2x - 3
g(x) = x^2 - 7
Substituting g(x) into f(x), we have:
f(g(x)) = 2(g(x)) - 3
= 2(x^2 - 7) - 3
= 2x^2 - 14 - 3
= 2x^2 - 17
Now we can set this expression equal to 25 and solve for x:
2x^2 - 17 = 25
Adding 17 to both sides:
2x^2 = 42
Dividing both sides by 2:
x^2 = 21
Taking the square root of both sides:
x = ±√21
Since we are looking for a real value of x, we can discard the negative square root.
Therefore, the value of x for which f(g(x)) = 25 is x = √21, which is approximately 4.58.
So, the correct answer is option D) 2.
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Community Answer
If f: R → R and g: R → R defined by f(x) = 2x + 3 andg(x) ...
f : R → R g : R → R
f(g) : R → R
f(x) = 2x + 3 g(x2) = x2 + 7
f(g(x)) = 2g(x) + 3
f(g(x)) = 2(x2 + 7) + 3
= 2x2 + 17
As it is given f(g(x)) = 25
Comparing both the eq, we get
2x2 + 17 = 25
2x2 = 8
x = +2
f(g) : R → R
f(x) = 2x + 3 g(x2) = x2 + 7
f(g(x)) = 2g(x) + 3
f(g(x)) = 2(x2 + 7) + 3
= 2x2 + 17
As it is given f(g(x)) = 25
Comparing both the eq, we get
2x2 + 17 = 25
2x2 = 8
x = +2
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If f: R → R and g: R → R defined by f(x) = 2x + 3 andg(x) = x2 + 7, then the value of x for which f(g(x)) = 25 isa)±3b)±1c)±4d)±2Correct answer is option 'D'. Can you explain this answer?
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