Answered

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If
f(x) = 2x3 + 6, which function satisfies
(fof-1) (x) = x and
(f-10 f)(x) = x? (1 point)

Sagot :

Answer:

Both are true.

Step-by-step explanation:

If f(x) = 2x³ + 6

To find the inverse of the given function,

Rewrite the function in the form of an equation,

y = 2x³ + 6

Interchange the variables x and y,

x = 2y³ + 6

Solve for y,

2y³ = x - 6

y = [tex]\sqrt[3]{\frac{(x-6)}{2}}[/tex]

Rewrite the equation in the form of a function,

[tex]f^{-1}(x)={\sqrt[3]{\frac{(x-6)}{2}}[/tex]

[tex](fof^{-1})(x)=f[f^{-1}(x)][/tex]

                  = [tex]2(\sqrt[3]{\frac{(x-6)}{2}})^3+6[/tex]

                  = (x - 6) + 6

                  = x

[tex](f^{-1}of)(x)=f^{-1}[{f(x)][/tex]

                  [tex]={\sqrt[3]{\frac{(2x^3+6-6)}{2}}[/tex]

                  [tex]={\sqrt[3]{\frac{(2x^3)}{2}}[/tex]

                  = x

Therefore, both the statements are true.

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