Answer:
The domain values are
1 ⇒ A
3 ⇒ C
4 ⇒ D
5 ⇒ E
7 ⇒ G
Step-by-step explanation:
In the function f(x);
- The domain is the values of x
- The range is the values of f(x)
∵ f(x) = -2x + 7
∵ The range is {5, 1, -1, -3, -7}
∴ f(x) = 5, 1, -1, -3, -7
→ To find x substitute f(x) by its values
∵ f(x) = 5
∴ 5 = -2x + 7
→ Subtract 7 from both sides
∴ 5 -7 = -2x + 7 - 7
∴ -2 = -2x
→ Divide both sides by -2 to find x
∵ [tex]\frac{-2}{-2}[/tex] = [tex]\frac{-2x}{-2}[/tex]
∴ 1 = x
∵ f(x) = 1
∴ 1 = -2x + 7
→ Subtract 7 from both sides
∴ 1 -7 = -2x + 7 - 7
∴ -6 = -2x
→ Divide both sides by -2 to find x
∵ [tex]\frac{-6}{-2}[/tex] = [tex]\frac{-2x}{-2}[/tex]
∴ 3 = x
∵ f(x) = -1
∴ -1 = -2x + 7
→ Subtract 7 from both sides
∴ -1 -7 = -2x + 7 - 7
∴ -8 = -2x
→ Divide both sides by -2 to find x
∵ [tex]\frac{-8}{-2}[/tex] = [tex]\frac{-2x}{-2}[/tex]
∴ 4 = x
∵ f(x) = -3
∴ -3 = -2x + 7
→ Subtract 7 from both sides
∴ -3 -7 = -2x + 7 - 7
∴ -10 = -2x
→ Divide both sides by -2 to find x
∵ [tex]\frac{-10}{-2}[/tex] = [tex]\frac{-2x}{-2}[/tex]
∴ 5 = x
∵ f(x) = -7
∴ -7 = -2x + 7
→ Subtract 7 from both sides
∴ -7 -7 = -2x + 7 - 7
∴ -14 = -2x
→ Divide both sides by -2 to find x
∵ [tex]\frac{-14}{-2}[/tex] = [tex]\frac{-2x}{-2}[/tex]
∴ 7 = x
∴ The domain of f(x) is {1, 3 , 4, 5, 7}
The domain values are
1 ⇒ A
3 ⇒ C
4 ⇒ D
5 ⇒ E
7 ⇒ G
