Evaluating Functions

Natalie asked the following:

could you please show how to work out this question:
f(x)=7-4x
(a) evaluate f(-2)
(b) given that f(t) = 9, find t

stuck on part (b)

Thanks for this, Natalie! Let's firstly check you did part (a) right.

f(x) is a function - literally a set of instructions of what to do to the value x.

So if the function f(x) is to do 7-4x, then any value of x can be operated on.

f(-2) means "do the function to x when x=-2"

So f(-2) = 7 - 4 (-2) = 7 + 8 = 15

Now to (b).

f(t) means let x=t (t is just another unknown number!)

The difference here is that we know what the function did to the number t: it gave the answer 9

So f(t) = 9 means that f(t) = 7 - 4t (i.e. you just need to set x=t)

But we know that f(t) = 9 so 7 - 4t = 9 is true.

So 7 = 9 + 4t
-2 = 4t
t = -2/4 = -0.5

I hope this is clear! Good luck!