The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .
What is inverse of a function?
An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.
now the given functions are,
f(x) = √(2x + 2) and
g(x) = (x^2 -2)/2
Now,
f{g(x)} = f{(x^2 -2)/2}
= √(2(x^2 -2)/2 + 2)
= √ x^2 -2 + 2
f{g(x)} = √ x^2
f{g(x)} = x
Now,
g{f(x)} = g{ √(2x + 2)}
= (√(2x + 2)^2 -2)/2
= (2x + 2) -2 /2
= 2x/2
f{g(x)} = x
Here we see that ,
f{g(x)} = g{f(x)}
Hence f and g are not inverses.
∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .
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