f(x) problem?

[aisha]

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

the answer was y=1/2(x+5)^(2)-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?

[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.

[Doc Al]

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

[ComputerGeek]

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.

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.

[James R]

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

the answer was y=1/2(x+5)^(2)-3

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 × _ - 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

[aisha]

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