Question

Use the graphs of f and g
Find the following values

Answer 1

After using the graph with the values of f and g we find the values as follows:

(i) (f+g)(-3) = 5

(ii) (g-f)(-2) = -1

(iii) (fg) (2) = -1

(iv) (g/f) (3) = 0

(v) (f o g) (1) = 1

(vi) (g o g)(-1) = 1

i) ( f +g ) (-3)

= ( f (-3) + g(-3) )

Values we got from the graph are:

f(-3) = 4

g(-3) = 1

After substituting these values in the given equation we get

( f + g) (-3) = 5

ii) ( g - f ) (-2)

= ( g(-2) - f(-2) )

Values we got from the graph are:

g(-2) = 2

f(-2) = 3

After substituting these values in the given equation we get

( g - f ) (-2) = - 1

iii) ( fg) (2)

= ( f(2) g(2))

Values we got from the graph are:

f(2) = -1

g(2) = 1

After substituting these values in the given equation we get

( fg)(2) = -1

iv) (g/f) (3)

( g(3) / f(3) )

Values we got from the graph are:

g(3) = 0

f(3) = - 3

After substituting these values in the given equation we get

( g / f ) (3) = 0

v) ( f o g ) (1)

= ( f(1) o g(1) )

Values we got from the graph are:

g(1) = 1

f(1) = 1

After substituting these values in the given equation we get

( f o g ) (1) = 1

vi) ( g o g ) (-1)

= ( g(-1) o g(-1) )

Values we got from the graph are:

g(-1) = 2

g(2) = 1

After substituting these values in the given equation we get

( g o g ) (-1) = 1

Answer 2

(i) 5

(ii) - 1

(iii) - 1

(iv) 0

(v) 1

(vi) 1

Explanation:

See the graph attached to this question.

The blue graph shows y = f(x) and the red graph shows y = g(x).

(i) (f + g)(- 3) = f(-3) + g(-3) = 4 + 1 = 5

(ii) (g - f)(- 2) = g(- 2) - f(- 2) = 2 - 3 = - 1

(iii) (fg)(2) = f(2) × g(2) = (- 1) × (1) = - 1

(iv)
`((g)/(f))(3) = (g(3))/(f(3)) = (0)/(- 3) = 0`

(v) (fog)(1) = f[g(1)] = f(1) = 1

(vi) (gog)(- 1) = g[g(-1)] = g(2) = 1 (Answer)