Question

If f is a function with domain [-11,13] and range (3,5].

What is the domain of f(6x+1)
And what is the range of 6f(x)+1

Answer 1

since f is defined only on [-11,13], you need
-11 <= 6x+13 <= 13
-4 <= x <= 0
so the new domain is [-4,0]

the range of 6f(x) + 1 is (6*3+1,6*5+1] = (19,31]

Answer 2

Hi oobleck,

Your answer for the range of 6f(x)+1 is correct.

But unfortunately the calculation of the domain for f(6x+1) isn't. I'm still trying to find the answer myself, I'm not sure where I'm tripping up.

Answer 3

well, I guess you didn't catch my glaring typo!
-11 <= 6x+1 <= 13
-2 <= x < 2
so the domain is [-2,2]

Answer 4

Thanks!