Find f(g(x)) f(x)=2x+1 ; g(x)=5x-4

$f (x) = 2 x + 1$ ; $g (x) = 5 x - 4$

Set up the composite result function.

$f (g (x))$

Evaluate $f (g (x))$ by substituting in the value of $g$ into $f$ .

$f (5 x - 4) = 2 (5 x - 4) + 1$

Simplify each term.

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Apply the distributive property.

$f (5 x - 4) = 2 (5 x) + 2 \cdot - 4 + 1$

Multiply $5$ by $2$ .

$f (5 x - 4) = 10 x + 2 \cdot - 4 + 1$

Multiply $2$ by $- 4$ .

$f (5 x - 4) = 10 x - 8 + 1$

Add $- 8$ and $1$ .

$f (5 x - 4) = 10 x - 7$

Find f(g(x)) f(x)=2x+1 ; g(x)=5x-4

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