Question

-Exponential and Logarithmic Functions- Write a function rule representing the following.

Answer 1

Given functions:

`f(x)=2x^2-1`
`g(x)=-5x`

The problem is asking for a multiplication of the functions, which can be done as follows:

`(fg)(x)=f(x)* g(x)`

Then, we have to multiply the functions:

`(fg)(x)=(2x^2-1)*(-5x)`

Simplifying we get:

`(fg)(x)=(2x^2\cdot-5x)-(1\cdot-5x)`
`(fg)(x)=-10x^3+5x`

In the second question, the problem is asking for a composition, which is equal to the following:

`(g\circ f)(x)=g(f(x))`

Then, in this case, we have to replace all the x in g(x) function by f(x):

`(g\circ f)(x)=-5\cdot(2x^2-1)`

Simplifying:

`(g\circ f)(x)=-10x^2+5`

Answer:

`(fg)(x)=-10x^3+5x`
`(g\circ f)(x)=-10x^2+5`