# If $f(x) = 3x-4$ (functions, highschool)

if $f(x) = 3x - 4$, find $x$ when $f(x) = 7$.

I would show my working out, but I have never experienced this type of question, nor have I been taught how to do it.

OK - $f(x)=7=3x-4$, can you solve this?

If $a=b$ then $a+3=b+3$ and $7a=7b$ and $a^{2}=b^{2}$ et cetera.

If you have an equality and both sides undergo the same 'mathematical protocol' then the equality holds. Formally: if $a=b$ and $g$ is some function defined on it then $g\left(a\right)=g\left(b\right)$.

Making use of that you find:

$\begin{array}{ccccc} 3x-4 & = & 7\\ 3x & = & 11 & & \text{addition of }4\text{ on both sides}\\ x & = & \frac{11}{3} & & \text{division by }3\text{ on both sides}\end{array}$

Applying this will definitely bring you further by 'questions of this type'.

You're given the function $f(x)=3x-4$ and need to find the value of $x$ when $f(x)=7$.

When you set 2 things equal, this means that you can replace one for another in an equation.

$f(x)=7$
$3x-4=7$
Can you solve this?

• I got x = 3 + 2/3, is that correct? Commented Jun 2, 2014 at 8:17
• @AnAverageBlokeNamedJoe Let's test it! If $x$ is $3+\frac{2}{3}$ then $3x-4=7$ matches if we replace $x$ with $3+\frac{2}{3}$. Lets try that $3\times(3+\frac{2}{3})-4=7\quad\quad(9+2)-4=7\quad\quad11-4=7\quad\quad7=7$ And $7$ is indeed equal to $7$. This means the result it correct. Commented Jun 2, 2014 at 8:39