A problem I'm facing is understanding the concept of inverse functions when multiplied to its original function. Here are the two functions provided:
f(x) = 2x + 3
h(x) = 2x
Here are the two questions being asked based on the functions given above:
(i) $hh^{-1}(x)$
(ii) $ff^{-1}(5)$
I did part (ii) by first by first making it y = 2x + 3, and then to x = 2y + 3. After this, I made it:
$\frac{x-3}{2}$ = y
I put 5 in the value for x to get the y value to become 1. After this, I made it f(1), where:
(2 $\times$ 1) + 3 = 5
So, I finally got the answer as 5.
For part (i), I was unsure as to how I could solve it using the same method.
y = 2$^x$
x = 2$^y$
Replace x with x I think just like how I replaced the x with 5 for part (ii). This would again result in
x = 2$^y$
I then make it h(x), which is equal to 2x. So, my final answer is 2x. However, the answer is x. I did not exactly understand how to get this. I know that the inverse of a function when multiplied to the original gives back the same variable/number. But, I wanted to know whether I could solve part (i) in a similar way to how I solved part (ii) and use this to further solve questions related to inverse functions.