Question

1. if h(x) = x² - 5x + 7, find each value. h(2) h(3) h(x) = (2)² - 5(2) + 7 = 4 - 10 + 7 = 1 h(2) = 1 h(3) = (3)² - 5(3) + 7 = 9 - 15 + 7 = 1 5. h(-5) h(-5) = (-5)² - 5(-5) + 7 = 25 + 25 + 7 = 57 6. (1/3)h(-8) 7. if g(x) = 1 - (3/4)x, find each value. 7. g(-12) g(-12) = 1 - (3/4)(-12) = 1 + 9 = 10 8. g(0) g(0) = 1 - (3/4)(0) = 1 9. -5 g(4) - 1 10. if h(x) = |1 - 7x|, find each value. 10. h(1) 11. h(-7) 12. 23 - h(9) 13. if f(x) = 8 - 5x, find each value. 13. f(4c) 14. f(2 - k) 15. f(4p + 3)

Explanation:

Step1: Evaluate $g(-12)$

Substitute $x=-12$ into $g(x)=1-\frac{3}{4}x$:
$g(-12)=1-\frac{3}{4}(-12)=1+9=10$

Step2: Evaluate $g(0)$

Substitute $x=0$ into $g(x)=1-\frac{3}{4}x$:
$g(0)=1-\frac{3}{4}(0)=1-0=1$

Step3: Evaluate $-5\cdot g(4)-1$

First find $g(4)$: $g(4)=1-\frac{3}{4}(4)=1-3=-2$
Then calculate: $-5(-2)-1=10-1=9$

Step4: Evaluate $h(1)$

Substitute $x=1$ into $h(x)=|1-7x|$:
$h(1)=|1-7(1)|=|1-7|=|-6|=6$

Step5: Evaluate $h(-7)$

Substitute $x=-7$ into $h(x)=|1-7x|$:
$h(-7)=|1-7(-7)|=|1+49|=|50|=50$

Step6: Evaluate $23-h(9)$

First find $h(9)$: $h(9)=|1-7(9)|=|1-63|=|-62|=62$
Then calculate: $23-62=-39$

Step7: Evaluate $f(4c)$

Substitute $x=4c$ into $f(x)=8-5x$:
$f(4c)=8-5(4c)=8-20c$

Step8: Evaluate $f(2-k)$

Substitute $x=2-k$ into $f(x)=8-5x$:
$f(2-k)=8-5(2-k)=8-10+5k=-2+5k$

Step9: Evaluate $f(4p+3)$

Substitute $x=4p+3$ into $f(x)=8-5x$:
$f(4p+3)=8-5(4p+3)=8-20p-15=-7-20p$

Answer:

1. $10$
2. $1$
3. $9$
4. $6$
5. $50$
6. $-39$
7. $8-20c$
8. $5k-2$
9. $-20p-7$