Respuesta :
Answer
a) g(-8) = 17
b) When g(x) = -7, x = 8
c) When f(x) = g(x), x = (2/3)
d) When f(x) = h(x), x = (1/20)
e) x-intercept of h(x) = (7/16)
Explanation
f(x) = 9x - 2
g(x) = 5 - 3x/2
h(x) = 4x - 7/4
(a) Find g(-8).
g(x) = 5 - 3x/2
g(-8) means the value of g(x) when x = -8
g(-8) = 5 - [3×-8/2]
= 5 - (-12)
= 5 + 12
= 17
(b) Find the value of x that makes g(x) = -7.
g(x) = 5 - 3x/2
When g(x) = -7,
5 - 3x/2 = -7
5 - (3x/2) - 5 = -7 - 5
-(3x/2) = -12
[tex]\begin{gathered} \frac{-3x}{2}=-12 \\ \text{Cross multiply} \\ -3x\text{ = 2}\times-12 \\ -3x\text{ = -24} \\ \text{divide both sides by -3} \\ \frac{-3x}{-3}=\frac{-24}{-3} \\ x\text{ = 8} \end{gathered}[/tex](c) Find the value of x that makes f(x) = g(x).
f(x) = 9x - 2
g(x) = 5 - 3x/2
When f(x) = g(x)
9x - 2 = 5 - (3x/2)
9x + (3x/2) = 5 + 2
(21x/2) = 7
[tex]\begin{gathered} \frac{21x}{2}=7 \\ \text{Cross multiply} \\ 21x\text{ = 2}\times7 \\ 21x=14 \\ \text{Divide both sides by 21} \\ \frac{21x}{21}=\frac{14}{21} \\ x=\frac{14}{21}=\frac{2}{3} \end{gathered}[/tex](d) Find the value of x that makes f(x) = h(x)
f(x) = 9x - 2
h(x) = 4x - 7/4
When f(x) = h(x)
9x - 2 = 4x - (7/4)
9x - 4x = 2 - (7/4)
5x = (1/4)
[tex]\begin{gathered} 5x=\frac{1}{4} \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{1}{4\times5} \\ x\text{ =}\frac{1}{20} \end{gathered}[/tex](e) Find the x-intercept of h(x).
h(x) = 4x - 7/4
The x-intercept is the value of x when h(x) = 0
When h(x) = 0
4x - (7/4) = 0
4x = (7/4)
[tex]\begin{gathered} 4x=\frac{7}{4} \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{7}{4\times4} \\ x=\frac{7}{16} \end{gathered}[/tex]Hope this Helps!!!
