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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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