Question

For all values of x,
f(x) = x/5 + 3
and
g(x) = 10x2 + 5
Work out fg(x).
Give your answer in the form ax2 + b where a and b are integers.

Answer 1

Answer:

2$x^{2}$+4

I would give a step by step explanation but it keeps saying I'm typing inappropriate words so message me if u need

Answer 2

Hence, The value of fg(x) in the form of ax2+b is 2x2+4.

What is composition of functions?

Composition of function is an operation in which we combine two or more function to generate a single function. In this question the function g is places in the place of x.

How to solve?

Given f(x)=x/5 +3

g(x)=10$x^{2}$ + 5

the composition of function ,

fg(x) = g(x)/5 + 3

fg(x) = (10$x^{2}$ + 5)/5 + 3

       = 2$x^{2}$+ 1 + 3

       = 2$x^{2}$ + 4

hence, fg(x)= 2$x^{2}$+4 where a=2 and b=4

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