# F(x) problem?

1. Dec 24, 2004

### aisha

if f(x)=x^2 write the equation for the transformed function y=2f(-1/2(x+5))-3

How do u get this answer? What happened to the 2f? and the - in 1/2?

Also how would the new function be graphed? What would it look like?

2. Dec 24, 2004

### quasar987

Here, 2f(-1/2(x+5))-3 does not mean 2 times f time -1/2(x+5) minus 3. It means, y is 2 times the function f(x)=x^2 where x is being replaced by the expression -1/2(x+5), minus 3.

3. Dec 24, 2004

### Staff: Mentor

A less confusing way of writing it would be: f(g) = g^2. Now y = 2f(g) - 3, where g = -1/2(x+5). So: y = 2f(g) - 3 = 2g^2 - 3. You finish it by substituting for g.

4. Dec 24, 2004

### ComputerGeek

I hate Math text books that set the students up with badly written problem sets just to make them harder than they really are.

though in all fairness, this could have been a starred question in the problem set.

5. Dec 25, 2004

### James R

The thing to realise about functional notation like f(x) is that x is a place holder. In other words, all of the following are equivalent definitions of the function f:

f(x) = x^2
f(y) = y^2
f(stuff) = (stuff)^2
f(_) = _^2

In your expression for y, we see f(-1/2(x+5))

Since f(anything) = anything^2, we get:

f(-1/2(x+5)) = (-1/2(x+5))^2 = 1/4(x+5)^2

Now y is another function, defined to be:

y(x) = 2x - 3

or

y(_) = 2 &times; _ - 3

We want y(f(-1/2(x+5))). Putting it all together:

y(f(-1/2(x+5))) = y(1/4(x+5)^2) = 2 [1/4(x+5)^2] - 3 = 1/2(x+5)^2 - 3

6. Dec 25, 2004

### aisha

Thanks everyone esp James I totally get it now, but it is sort of complicated at first.