Find f(g(x)) f(x)=5x-1 and g(x)=5x^2-1

$f (x) = 5 x - 1$ and $g (x) = 5 x^{2} - 1$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 x^{2} - 1)$ by substituting in the value of $g$ into $f$ .

$f (5 x^{2} - 1) = 5 (5 x^{2} - 1) - 1$

Step 3

Simplify each term.

Apply the distributive property.

$f (5 x^{2} - 1) = 5 (5 x^{2}) + 5 \cdot - 1 - 1$

Multiply $5$ by $5$ .

$f (5 x^{2} - 1) = 25 x^{2} + 5 \cdot - 1 - 1$

Multiply $5$ by $- 1$ .

$f (5 x^{2} - 1) = 25 x^{2} - 5 - 1$

Step 4

Subtract $1$ from $- 5$ .

$f (5 x^{2} - 1) = 25 x^{2} - 6$