Question

Suppose $a(x) = 3x - 7$ and $b(x) = 2 - x^3$. What is the value of $a(b(3)) - b(a(3))$?

Answer 1

Answer:

-76

Step-by-step explanation:

b(3)=2-3^3 = -25.

So a(b(3))=a(-25)=3(-25)-7=-82.

a(3)=3(3)-7=2.

So b(a(3))=2-2^3 = -6.

Therefore, the value of the desired expression is -82-(-6)=-76

Answer 2

The value of the required function $a(b(3)) - b(a(3))$ is (-88).

What is a function?

"A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}

A relation is said to be a function if every element of set A has one and only one image in set B.

A function is a relation from a non-empty set B such that the domain of a function is A and no two distinct ordered pairs in f have the same first element."

Given two functions are:

$a(x) = 3x - 7\\b(x) = 2 - x^{3}$

When the value of 'x' is 3, then the values of the given two functions are:

$a(3) \\= 3x - 7\\= 3(3)-7\\= 9-7\\= 2$

$b(3)\\= 2 - x^{3}\\= 2-(3)^{3}\\= 2-27\\= -25$

Now the value of the required function is:

$a(b(3)) - b(a(3))\\= a(-25)-b(2)\\= [3(-25)-7]-[2-2^{3}]\\= (-75-7)-(2-8)\\= -82-6\\= -88$

Therefore, the value of the required function is (-88).

Learn more about a function here:

https://brainly.com/question/12431044

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