# Thread: Help with functions and range.

1. ## Help with functions and range.

Hello there I'm really hoping someone can help. I've just returned to studying maths after a 20 year break and I am really struggling to get to grips with this question.

I've managed to get f(-4)=1 but don't really understand how to tackle the rest of the question . It's question number 3 but will have similar problems with q4 as it's very similar

2. ## Re: Help with functions and range.

Okay, I presume that you wrote $\displaystyle f(x)= \frac{2x+ 3}{x- 1}= 1$ and then solved that equation for x: multiply both sides by x- 1 to get $\displaystyle 2x+ 3= x- 1$. Subtract x from both sides: $\displaystyle x+ 3= -1$. Subtract 3 from both sides: $\displaystyle x= -4$.

The rest of the problem asks you to "find a (in terms of b) such that f(a)= b." Do the same thing as before: $\displaystyle f(x)= \frac{2x+ 3}{x- 1}= b$. Multiply both sides by x- 1 to get $\displaystyle 2x+ 3= b(x- 1)= bx- b$. Subtract bx from both sides: $\displaystyle 2x- bx+ 3= -b$. Subtract 3 from both sides $\displaystyle 2x- bx= (2- b)x= -3- b$. Divide both sides by 2- b: $\displaystyle x= \frac{-3- b}{2- b}$. Can you see why b cannot be equal to 2?

3. ## Re: Help with functions and range.

Hey there thanks for your response I think it was the wording of the question that got me. What I did is substitute the x for a then made the function equal to one so got the value of a.

Then I tried to do this (2a)b+3/(a)b-1. I don't know why I didn't just make the original function equal to b. I just didn't understand the wording and what a in terms of b actually meant.

I understand that b can't equal 2 as the function would be undefined as you can't divide by zero. How do I write this in a mathematical way, is b just any number except 2?

4. ## Re: Help with functions and range.

Originally Posted by Chriscbhoy
I understand that b can't equal 2 as the function would be undefined as you can't divide by zero.
How do I write this in a mathematical way, is b just any number except 2?
Given $f(x) = \dfrac{{2x + 3}}{{x - 1}}$ then if $b \ne 2$ it follows that $f\left( {\dfrac{{ - 3 - b}}{{2 - b}}} \right) = b$.