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# Functions C3 Help

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1. 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!

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2. (Original post by james0902)
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!

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3a : What is fg(a) ?

Once you've found this, set it equal to 100 to find a.
3. EDIT - Help with question 4 would also be appreciated.

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4. Remember, composite function is the same as - i.e. substituting the function as the variable in the function .

E.g.

If and , the function .

So if we had to find the value of for which , we get .

5. (Original post by notnek)
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)

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6. (Original post by james0902)

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)

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doesn't mean .

It means .

If you're not sure how to deal with this then I recommend trying easier composite functions questions before attempting this one.
7. Ok so we know that f(x)=ax+b (equation 1) and ff(x)=9x-28 (equation 2). Using equation one, form an equation for ff(x) and set that equal to equation 2. Then set the x terms equal to eachother.
8. (Original post by james0902)

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)

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If it helps, and instead of , say that . This means that

Now find an expression for . This gives you .

Now, you can substitute as because .

So we get .
Now substitute as .

You get . Set this equal to 100 and solve for x.
9. (Original post by The_Big_E)
If it helps, and instead of , say that . This means that

Now find an expression for . This gives you .

Now, you can substitute as because .

So we get .
Now substitute as .

You get . Set this equal to 100 and solve for 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.
10. fg(x) does not mean multiply f by g(x)
11. (Original post by the bear)
fg(x) does not mean multiply f by g(x)
12. (Original post by HapaxOromenon3)
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.
Ah yes, didn't think of using inverse function. Nice.

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