Find f(g(x)) f(x)=6x+1 , g(x)=8x+7

$f (x) = 6 x + 1$ , $g (x) = 8 x + 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (8 x + 7)$ by substituting in the value of $g$ into $f$ .

$f (8 x + 7) = 6 (8 x + 7) + 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (8 x + 7) = 6 (8 x) + 6 \cdot 7 + 1$

Multiply $8$ by $6$ .

$f (8 x + 7) = 48 x + 6 \cdot 7 + 1$

Multiply $6$ by $7$ .

$f (8 x + 7) = 48 x + 42 + 1$

Step 4

Add $42$ and $1$ .

$f (8 x + 7) = 48 x + 43$