Chapter 3.8, Problem 36WE

To determine

To Calculate:The value of Functions.

Answer to Problem 36WE

The Value of function is $f\left(g\left(-1\right)\right)=8,g\left(f\left(-1\right)\right)=1$ .

Explanation of Solution

Given Information:In this question, Functions $f(x)=x^2-1$ and $g(x)=1-2x$ are given to calculate the value functions.

Concept Used:

Following steps must be taken to calculate the value of the function.

Step $1$ : $f\left(g\left(x\right)\right)=f\left(p\right)$ Where $p$ is the value of $g(x)$ at point $x$ .

Step $2$ : $g\left(f\left(x\right)\right)=g\left(p\right)$ Where $p$ is the value of $f(x)$ at point $x$ .

Calculation:

Function is given as:

Function is $f(x)=x^2-1$ and $g(x)=1-2x$ .

As per the above-mentioned concept

  $g(-1)=1-2.\left(-1\right)=1+2=3$ , $f(-1)={\left(-1\right)}^2-1=1-1=0$

  $f\left(g\left(-1\right)\right)=f\left(3\right)={\left(3\right)}^2-1=9-1=8$ .

  $g\left(f\left(-1\right)\right)=g\left(0\right)=1-2.0=1$ .

So $f\left(g\left(-1\right)\right)=8,g\left(f\left(-1\right)\right)=1$ .

Conclusion:

The value of Functions are $f\left(g\left(-1\right)\right)=8,g\left(f\left(-1\right)\right)=1$