Question 647815
You need to plug in the inner value first and then you can do it all together.

Original equations: {{{f(x)=x^2-1}}} and {{{g(x)=1-2x}}}

Find {{{f(g(-1))}}} and {{{g(f(-1))}}}

Step 1: We'll begin by doing this equation first: {{{f(g(-1))}}}

You're going to want to solve {{{g(-1)}}} first.

{{{g(-1)=1-2(-1)}}}

Step 2: Simplify

{{{g(-1)=1+2}}}
{{{g(-1)=3}}}

So, now we know that {{{g(-1)=3}}}, so let's replace '3' into the {{{f(x)=x^2-1}}} equation.

Step 1: Replace '3' into the equation

{{{f(3)=3^2-1}}}

Step 2: Simplify

{{{f(3)=9-1}}}
{{{f(3)=8}}}

The answer to {{{f(g(-1))}}} is 8.

Let's do the other equation now ({{{g(f(-1))}}})

You're going to want to solve {{{f(-1)}}} first.

Step 1: Replace '-1' into the f(x) equation

{{{f(-1)=(-1)^2-1}}}
{{{f(-1)=1-1}}}
{{{f(-1)=0}}}

Now we know that {{{f(-1)=0}}}, so let's replace '0' into the {{{g(x)=1-2x}}} equation.

Step 1: Replace '0' into the equation

{{{g(0)=1-2(0)}}}

Step 2: Simplify

{{{g(0)=1-0}}}
{{{g(0)=1)}}}

The answer to {{{g(f(-1))}}} is 1.