Question

Drag each tile to the correct box.

Use these functions to place the function compositions in order from least to greatest value.
f(x) = 2x^2
g(x) = x − 2

Answer 1

(g ο f)(0) < (f ο g)(3.5) < (g ο f)(- 2) < (f ο g)(0) < (g ο f)(3.5) < (f ο g)(-2)

Explanation:

We are given that f(x) = 2x² and g(x) = x - 2

Therefore, (f ο g)(x) = f[]g(x)] = 2(x - 2)² ......... (1)

and (g ο f)(x) = g[f(x)] = 2x² - 2 ........... (2)

Therefore, (f ο g)(-2) = 32 {from equation (1)}

(f ο g)(3.5) = 4.5 {From equation (1)}

And (f ο g)(0) = 8 {From equation (1)}

Now, (g ο f)(- 2) = 6 {From equation (2)}

(g ο f)(3.5) = 22.5 {From equation (2)}

And (g ο f)(0) = -2 {From equation (2)}

Therefore, if we arrange those values from least to greatest value, then we will get

(g ο f)(0) < (f ο g)(3.5) < (g ο f)(- 2) < (f ο g)(0) < (g ο f)(3.5) < (f ο g)(-2) (Answer)