Question

Jamaal is using a photo-editing computer program. He sets up the "F1" key to perform a 20% enlargement in both dimensions. He sets up the "F2" key to increase the picture size by 2cm in both dimensions. Then Jamaal sets up "F3" to do "F1" followed by "F2".

What is the equivalent function for a picture xcm by xcm?

A f3(x)=f2(f1(x))=1.2x+2
B f2 (x)+(fx+f1) (x)=2.2x=2
C f3 (x)=f1(f2(x))=1.2x+2.4
D f3 (x) = (f2 *f1)(x)=1.2x^2+2.4x

Answer 1

A f3(x)=f2(f1(x))=1.2x+2

Explanation:

The "F1" key is to perform a 20% enlargement in both dimensions. So, first the function F1 increases the dimension x by 20%. That is, our new dimension x' is now the initial dimension plus the increase. The initial dimension is x and the increase is 20% of x = 0.2x. So, x' = x + 0.2x = 1.2x. So, F1(x) = x' = 1.2x

Then, the "F2" key is to increase the picture size by 2cm in both dimensions. So, the function F2 works on x' and add 2 cm to it. So, our new dimension is thus x" = x' + 2.

So F2(x') = x" = x' + 2 = F1(x) + 2

F2(F1(x)) = x' + 2 = 1.2x + 2

F3(x) = F2(F1(x)) = 1.2x + 2

F3(x) = 1.2x + 2.

So, the equivalent function for a picture x cm by x cm is F3(x) = F2(F1(x)) = 1.2x + 2.