Functions C3 Help

Hi,
So we're going back to school on Monday and I have some work to do before we go back but I'm a bit rusty because we've just had summer! If anyone can help me out / talk through part 3a 3b and 3c of this question it would be appreciated!


Posted from TSR Mobile

3a : What is fg(a) ?

Once you've found this, set it equal to 100 to find a.

So this is where I'm at with the working I've put the 100 over to this side but I'm just struggling with solving this! Any help is appreciated (for question 3a)


Posted from TSR Mobile

So this is where I'm at with the working I've put the 100 over to this side but I'm just struggling with solving this! Any help is appreciated (for question 3a)


Posted from TSR Mobile

If it helps, $f(x) = x^2$ and instead of $g(x) = 3x - 2$, say that $y = 3x - 2$. This means that $g(x) = y$

Now find an expression for $f(y)$. This gives you $f(y) = y^2$.

Now, you can substitute $y$ as $g(x)$ because $g(x) = y$.

So we get $f(g(x)) = (g(x))^2$.
Now substitute $g(x)$ as $3x - 2$.

You get $fg(x) = (3x - 2)^2$. Set this equal to 100 and solve for x.

fg(x) does not mean multiply f by g(x)

An easier way is fg(a) = 100 -> g(a) = f^-1(100) = +/-10 -> 3x-2 = +/-10 -> 3x = 12 or -8 -> x = 4 or -8/3.