If {f}(x)=3 x+10, {~g}(x)=x²-1, then ({fog})^{-1}(x)=

Correct Answer is : (x−73)12≤ft(x-7/3)¹/2}(3x−7)21

Correct Answer is : (x−73)12≤ft(x-7/3)¹/2}(3x−7)21

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MHTCET 23 Apr 2025 Shift 1 Paper

Question : 142 of 150

Marks: +1, -0

\mathrm{f}(x)=3 x+10, \quad \mathrm{~g}(x)=x^{2}-1

(\mathrm{fog})^{-1}(x)=

Solution:

Concept:

Composition of functions and finding the inverse of the composite function.

Explanation:

First, find

(f \circ g)(x)

(f \circ g)(x) = f(g(x)) = f(x^2 - 1)

= 3(x^2 - 1) + 10 = 3x^2 - 3 + 10 = 3x^2 + 7

Let

y = (f \circ g)(x) = 3x^2 + 7

Solve for

x

in terms of

y

y - 7 = 3x^2

x^2 = \frac{y - 7}{3}

x = \left(\frac{y - 7}{3}\right)^{1/2}

Since

x = (f \circ g)^{-1}(y)

, replace

y

x

(f \circ g)^{-1}(x) = \left(\frac{x - 7}{3}\right)^{1/2}

Answer:

\left(\frac{x - 7}{3}\right)^{1/2}

Therefore, option B is correct.

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