Question

Given f (x) = 4x-3, g(x) = x^3 +2x
Find (f-g) (4)

Answer 1

Explanation:

I love this question!

So there are a couple different ways of solving this. You feel free to ignore whichever one makes less sense.

Subtracting First

The first option is taking f(x) and g(x) and subtracting them, then introducing the number.

The calculation:

f(x) - g(x)

Substitute.

4x - 3 - (x^3 + 2x)

Multiply out the negative.

4x - 3 - x^3 - 2x

Rewrite.

-x^3 + 4x - 2x - 3

Simplify.

-x^3 + 2x - 3

Then, replace x with 4.

-(4)^3 + 2(4) - 3

Simplify.

-64 + 8 - 3

Add.

-59

Making x = 4 first

Here, we'll do what's on the tin. Find f(4) and g(4), then subtract them.

f(x) = 4x - 3

f(4) = 4(4) - 3

f(4) = 16 - 3

f(4) = 13

Then find g(4):

g(x) = x^3 + 2x

g(4) = (4)^3 + 2(4)

g(4) = 64 + 8

g(4) = 72

Then, subtract these two:

f(4) - g(4) = 13 - 72

f(4) - g(4) = -59

Answer:

Either way, the answer is -59

Answer 2

`(f-g)(4) = -59`

Explanation:

We are given the two functions:

`f(x)=4x-3\text{ and } g(x) = x^3 +2x`

And we want to find the value of:

`(f-g)(4)`

Recall that this is equivalent to:

`(f-g)(4) = f(4) - g(4)`

Find f(4):

`f(4) = 4(4)-3 = 13`

And find g(4):

`g(4) = (4)^3 + 2(4) =72`

Substitute:

`(f-g)(4) = (13)-(72)`

And subtract. Hence:

`(f-g)(4) = -59`