- #1
trevor
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Let f(x) = x^{2}-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f^{-1} (x) = g^{-1}(x)
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f^{-1} (x) = g^{-1}(x)
trevor said:Let f(x) = x^{2}-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f^{-1} (x) = g^{-1}(x)
Joppy said:Hi trevor. What have you tried so far? :)
The purpose of the function (f º g)(x) is to find the composition of two functions, f(x) and g(x). This means that the output of g(x) is used as the input for f(x), resulting in a new function.
To find the composition of two functions, you need to plug the inner function (g(x)) into the outer function (f(x)). In this case, (f º g)(x) = f(g(x)).
To plug in values for x in a composition of functions, you need to first evaluate the inner function (g(x)) using the given value for x. Then, take the result and plug it into the outer function (f(x)) to get the final output.
Yes, the order of the functions can be rearranged in a composition. However, the resulting function may be different depending on the order of the functions.
To solve for (f º g)(2), first evaluate g(2) to get a specific value. Then, plug that value into f(x) to get the final output. In this case, (f º g)(2) = f(g(2)) = f(-1) = (-1)^2 - 7 = -6.