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Firstly, can someone please recommend me a good online course to help me with function notation? My maths exercise books gives us various types of question but does not show us how to solve each type of one.

Given $f(x) = x^2 + 3$ find any values of x for which $f(x) = 28$. I don't know how to solve this, but I do understand from the question that the answer is 5 and -5. What is the 'method' of solving this?

second question:

If $f(x) = 3^x$, find $x$ when $f(x) = 1/27$

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You can view a function such as your given$f(x) = x^2+3$ as an equality.

It is very similar to $y=x^2+3$, if you're more familiar with that.

A function whose highest degree is $2$, as you may know, is a parabola, and a parabola has $y$ values that are equal at distances that are equidistant from the vertex (the value of $x$ which gives the minimum or maximum $y$ value of a parabola, depending on if it is increasing or decreasing, respectively--as well as being the only point whose $y$ value is unique.

For example, in $f(x) = x^2$, for values $x=2$ and $x=-2$, the value of $y$ is equal to $4$.

The first google search for function notation brings up this link.

It may help you a bit with understanding function notation.

Also, don't forget to check-mark an answer as accepted once you have found one which suits your liking and gives you adequate explanation of your question topic, in order to give closure to the topic (I note this as you are a new member, just a handy tip).

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For the first question : if $f(x)=x^2+3=28$, then $x^2=28-3=25=(\pm 5)^2$. Then $x=\pm 5$.

For the second question : if $f(x)=3^x=\frac{1}{27}$, then $3^x=\frac{1}{3^3}=3^{-3}$. Then $x=-3$.

Is this clearer for you ?

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