Question

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (9 - 1)(3)?

Answer 1

(g − f) ( 3 ) = 23

Explanation:

( g − f ) ( x ) = g ( x ) − f ( x )

= 6 x − ( 4 − x 2 )

= x 2 + 6 x − 4

to evaluate ( g - f ) ( 3 ) substitute x = 3 into ( g − f ) ( x )

( g − f ) = ( 3 ) 2 + ( 6 x 3 ) - 4 =23

Answer 2

For this case we have the following functions:

`f (x) = 4-x ^ 2\\g (x) = 6x`

By definition we have to:

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

Then, we find
`(f-g) (x):`

`f (x) -g (x) = 4-x ^ 2-6x = -x ^ 2-6x 4`

We evaluate the function in 3:

`(f-g) (3) = - (3) ^ 2-6 (3) 4 = -9-18 4 = -27 4 = -23`

Now we find
`(g-f) (x):`

`g (x) -f (x) = 6x- (4-x ^ 2) = 6x-4 x ^ 2 = x ^ 2 6x-4`

We evaluate the function in 3

`(g-f) (3) = 3 ^ 2 6 (3) -4 = 9 18-4 = 23`

Answer:

`(f-g) (3) = - 23\\(g-f) (3) = 23`