SOLUTION: If f(x)=2x+3 g(x)=x-1 are two functions defined on a set of real number show that [fg(x)] raise to power -1=g raise to power-1[f raise to power-1(x)]. NOTE raise to power is i

Algebra ->  Functions -> SOLUTION: If f(x)=2x+3 g(x)=x-1 are two functions defined on a set of real number show that [fg(x)] raise to power -1=g raise to power-1[f raise to power-1(x)]. NOTE raise to power is i      Log On


   

Question 707097: If f(x)=2x+3
g(x)=x-1 are two functions defined on a set of real number show that [fg(x)] raise to power -1=g raise to power-1[f raise to power-1(x)]. NOTE raise to power is inverse
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
That is usually not its meaning for functions. Similar notation but with different meaning for a number than for a function.

a is a real number. There is a number which if multiplied by a gives the product, 1. a%28a%5E-1%29=1, and we say that a%5E-1 is the multiplicative inverse of a.

g(x) is a function which uses the independant variable number, x. This means you give the function a number or a value as input and g is then evaluated at that given input. There is another function which will undo what g(x) does and give you x as the result. Call this new function, g%5E-1%28x%29. This is the inverse of g(x). It does NOT mean 1%2F%28g%28x%29%29. What we have with these two inverse functions is that g%28g%5E-1%28x%29%29=x, and g%5E-1%28g%28x%29%29=x.

[the little operator dot in the above typeset expressions were unintended. Books usually permit a much better job of this.]