Question #d780a

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Answer 1 · 2017-07-05T08:49:24

$(g circ f)^(- 1) = - frac(1)(28) (x + 11)$

We have: $f(x) = 4 x + 3$ and $g(x) = - 7 x + 10$

First, let's evaluate $g circ f$ :

$Rightarrow g circ f = g (f(x))$

$Rightarrow g circ f = g (4 x + 3)$

$Rightarrow g circ f = - 7 (4 x + 3) + 10$

$Rightarrow g circ f = - 28 x - 21 + 10$

$Rightarrow g circ f = - 28 x - 11$

Let's suppose $y = g circ f$ .

We must now find the inverse of $y$ :

$Rightarrow y = - 28 x - 11$

Interchanging variables:

$Rightarrow x = - 28 y - 11$

Let's solve for $y$ :

$Rightarrow x + 11 = - 28 y$

$Rightarrow y = - frac(1)(28) (x + 11)$

$therefore (g circ f)^(- 1) = - frac(1)(28) (x + 11)$