Given the functions b(x)=√(x) and c(x)=2x+9, find each of the following and simplify. a) Find b(c(x)) b) Find x if b(c(x)) = 5.

Question

Given the functions b(x)=
`√(x)` and c(x)=2x+9, find each of the following and simplify.

a) Find b(c(x))
b) Find x if b(c(x)) = 5.

Answer 1

a) The value of b(c(x)) = √(2x + 9).

b) The value of x if b(c(x)) = 5 is 8.

Step-by-step explanation:

To find b(c(x)), we substitute c(x) into the function b(x).

So, b(c(x)) = b(2x + 9).

Since b(x) = √x, we have:

b(c(x)) = √(2x + 9).

To find x if b(c(x)) = 5, we set √(2x + 9) = 5 and square both sides to get:

2x + 9 = 25.

Then, we solve for x:

2x = 16 and x = 8.