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Range of a composite function

This type of question, asked 2 times: 29 Jan 2024, 4 Apr 2025. All 2 questions below, oldest first.

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  1. Question 1

    29 Jan 2024

    63
    If f(x)={2+2x,−1≤x<01−x3,0≤x≤3;g(x)={−x,−3≤x≤0x,0<x≤1 f(x) =\left\{ \begin{matrix} 2 + 2x, - 1 \leq x < 0 \\ 1 -\frac{x}{3},0 \leq x \leq 3 \end{matrix};g(x) =\left\{ \begin{matrix} - x, - 3 \leq x \leq 0 \\ x,0 < x \leq 1 \end{matrix} \right.\ \right., then range of (fog(x))(fog(x)) is

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  2. Question 2

    4 Apr 2025

    51
    Let f, g:(1,∞)→Rf,\text{ }g:(1,\infty) \rightarrow\mathbb{R} be defined as f(x)=2x+35x+2f(x) =\frac{2x+ 3}{5x+ 2} and g(x)=2−3x1−xg(x) =\frac{2 - 3x}{1 -x}. If the range of the function f∘g:[2,4]→Rf\circ g:\lbrack 2,4\rbrack \rightarrow\mathbb{R} is [α,β]\lbrack\alpha,\beta\rbrack, then 1β−α\frac{1}{\beta-\alpha} is equal to.

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