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Find a function or its value from a given composition

This type of question, asked 4 times: 29 Jun 2022, 25 Jan 2023, 13 Apr 2023, 28 Jan 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    29 Jun 2022

    180
    Let f(x)f(x) and g(x)g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x))=8x2−2xf(g(x)) = 8x^{2}- 2x, and g(f(x))=4x2+6x+1g(f(x)) = 4x^{2}+ 6x + 1, then the value of f(2)+g(2)f(2) + g(2) is

  2. Question 2

    25 Jan 2023

    82
    For some a,b,c∈Na,b,c \in N, let f(x)=ax−3f(x) = ax - 3 and g(x)=xb+c,x∈Rg(x) =x^{b}+ c,x \in R. If (f∘g)−1(x)=(x−72)1/3(f \circ g)^{- 1}(x) =\left( \frac{x - 7}{2} \right)^{1/3}, then (f∘g)(ac)+(g∘f)(b)(f \circ g)(ac) + (g \circ f)(b) is equal to

  3. Question 3

    13 Apr 2023

    74
    For x∈Rx\in R, two real valued functions f(x)f(x) and g(x)g(x) are such that, g(x)=x+1g(x) =\sqrt{x}+ 1 and f∘g(x)=x+3−xf \circ g(x) = x + 3 -\sqrt{x}. Then f(0)f(0) is equal to

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  4. Question 4

    28 Jan 2026 S1

    51
    If g(x)=3x2+2x−3,f(0)=−3g(x) = 3x^{2}+ 2x- 3,f(0) = - 3 and 4g(f(x))=3x2−32x+724g(f(x)) = 3x^{2}- 32x + 72, then f( g(2))f(\text{ }g(2)) is equal to:

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