Question

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

Answer 1

Answer:

$-\frac{1}{4}$

Step-by-step 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 =$-\frac{1}{4}$

Answer 2

Answer:

-0.25

Step-by-step 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