QuestionFind the composite function for $f(x)=4 x^{2}+5 x+6$ and $g(x)=5 x-3$ : $(g \circ f)(x)$ .

Studdy Solution

STEP 1

Assumptions1. We have two functions, $f(x) =4x^ +5x +6$ and $g(x) =5x -3$ . . We are asked to find the composite function $(g \circ f)(x)$ , which means we need to substitute $f(x)$ into $g(x)$ .

STEP 2

The composite function $(g \circ f)(x)$ is defined as $g(f(x))$ . This means we substitute $f(x)$ into $g(x)$ wherever we see an $x$ .

STEP 3

Substitute $f(x)$ into $g(x)$ .
$(g \circ f)(x) = g(f(x)) =5f(x) -3$

STEP 4

Substitute $f(x)$ into the equation from3.
$(g \circ f)(x) =(4x^2 +x +6) -3$

STEP 5

Expand the equation from4.
$(g \circ f)(x) =20x^2 +25x +30 -3$

STEP 6

implify the equation from5.
$(g \circ f)(x) =20x^2 +25x +27$ The composite function $(g \circ f)(x)$ is $20x^2 +25x +27$ .

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