Question

For all values of x, f(x)=2x^2 and g(x)= x+1
Solve fg(x) = gf(x)

Answer 1

`-(1)/(4)`

Explanation:

Work out fg(x)

To work out fg(x), put the g function into the f function so, the x in f(x) is equal to the x+1 (from the g function) so:

`2(x+1)^(2) = 2 (x^(2) +2x+1) = 2x^(2) + 4x +2`

So fg(x) =
`2x^(2) + 4x +2`

Work out gf(x)

Do this by substituting the f(x) equation into the g(x) which is:

`(2x^(2) )+1`

So gf(x) =
`(2x^(2) )+1`

Work out x

And since fg(x) = gf(x),

`2x^(2) + 4x +2` =
`(2x^(2) )+1`

4x = -1

x =
`-(1)/(4)`

Answer 2

-0.25

Explanation:

→ Find fg(x)

2 ( x + 1 )² = 2x² + 4x + 2

→ Find gf(x)

2x² + 1

→ Equate them

2x² + 1 = 2x² + 4x+ 2

→ Move everything to the right hand side

0 = 4x + 1

→ Solve

x = -0.25