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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
Answer:
[tex]-\frac{1}{4}[/tex]
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:
[tex]2(x+1)^{2} = 2 (x^{2} +2x+1) = 2x^{2} + 4x +2[/tex]
So fg(x) = [tex]2x^{2} + 4x +2[/tex]
Work out gf(x)
Do this by substituting the f(x) equation into the g(x) which is:
[tex](2x^{2} )+1[/tex]
So gf(x) = [tex](2x^{2} )+1[/tex]
Work out x
And since fg(x) = gf(x),
[tex]2x^{2} + 4x +2[/tex] = [tex](2x^{2} )+1[/tex]
4x = -1
x =[tex]-\frac{1}{4}[/tex]