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You can graph the function and if it passes the vertical line test, it's one-to-one.
 
 
Does f(a) = f(b) imply that a=b?
 
f(a) = (a+5)^3
f(b) = (b+5)^3
 
If (a+5)^3 = (b+5)^3...
 
Cube root of both sides:
 
a+5 = b+5
 
Subtract 5 from both sides:
 
a = b.   It's one-to-one.
 
Note that the parent function is y = x^3, which is one-to-one.
 
It is shifted 5 units to the left, so it crosses the x axis at (-5, 0).  Down to the left and up to the right.
 
 
To get the inverse function, exchange x and y and solve for y:
 
x = (y+5)^3
 
Take the cube root of both sides:
 
x^(1/3) = y+5
 
y = x1/3 - 5
 
 
If they are inverses, once you graph them, they should be reflections of each other across the line y=x.

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