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Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b?
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Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) co...
For nested functions like f(g(x)), we must work from inside out. So we start with the function g(x) as the input value for function f(x).
Given: g(x) = 7x + b, and f(x) = sqrt(x).
So, we get, f(g(x)) = sqrt(7x + b).
We are also given that y = f(g(x)) function passes through coordinates (4,6), so let us use the value at this coordinate in the above function. Here x = 4, and y = 6. We get:
6 = sqrt(7 x 4 + b)
We can square both sides to eliminate the square root. We get:
36 = 28 + b
Or, 36 - 28 =
Or, b = 8
This question is part of UPSC exam. View all Class 10 courses
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Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) co...
Explanation:
Given:
- f(x) = √x
- g(x) = 7x + b
- y = f(g(x))
- Point (4,6) lies on y = f(g(x))
Step 1: Find g(x)
Since g(x) = 7x + b, we can substitute this into f(x) to get y = f(7x + b).
Step 2: Find y = f(g(x))
Given that y = f(g(x)), we have y = √(7x + b).
Step 3: Substitute the point (4,6)
Since the point (4,6) lies on y = √(7x + b), we can substitute x=4 and y=6 into the equation to get 6 = √(7(4) + b).
Step 4: Solve for b
Now, we can solve for b:
6 = √(28 + b)
6 = √28 + √b
6 = √28 + √b
6 - √28 = √b
36 - 28 = b
b = 8
Therefore, the value of b is 8.
Given:
- f(x) = √x
- g(x) = 7x + b
- y = f(g(x))
- Point (4,6) lies on y = f(g(x))
Step 1: Find g(x)
Since g(x) = 7x + b, we can substitute this into f(x) to get y = f(7x + b).
Step 2: Find y = f(g(x))
Given that y = f(g(x)), we have y = √(7x + b).
Step 3: Substitute the point (4,6)
Since the point (4,6) lies on y = √(7x + b), we can substitute x=4 and y=6 into the equation to get 6 = √(7(4) + b).
Step 4: Solve for b
Now, we can solve for b:
6 = √(28 + b)
6 = √28 + √b
6 = √28 + √b
6 - √28 = √b
36 - 28 = b
b = 8
Therefore, the value of b is 8.
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Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b?
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Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b?.
Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the function f(x) = √x and g(x)=7x+b.In the standard (X,y) coordinate plane y=f(g(x)) passes through (4,6) ?what is the value of b?.
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