Question

30 points
1)The function g is defined by g(x)=cx−3, where c is a constant. Find c, if the value of g(x) at x=0.5 is equal to −1.
2)The function h is defined by h(x)=(20x−k)÷x+50, where k is a constant. Find k, if the value of ℎ at x=20 is equal to 65.

Answer 1

Answer:

1) The value of c is given by

$c=4$

2) The value of k is given by

$k=-4150$

Step-by-step explanation:

Given that function g is defined by $g(x)=cx-3$ , where c is a constant.

To find c:

Also given that value of g(x) at x=0.5 is equal to -1

ie., $g(0.5)=-1$

At x=0.5

$g(0.5)=c(0.5)-3=-1$

$(0.5)c-3=-1$

$(0.5)c=-1+3$

$(0.5)c=2$

$c=\frac{2}{0.5}$

$c=\frac{2}{\tfrac{1}{2}}=2\times \frac{2}{1}$

Therefore $c=4$

2) Given that function h is defined by $h(x)=\frac{20x-k}{x+50}$ , where k is a constant.

To find k:

Also given that value of h(x) at x=20 is equal to 65

ie., $h(20)=65$

At x=20

$h(20)=\frac{20(20)-k}{20+50}=65$

$400-k=65(70)$

$-k=4550-400$

$-k=4150$

Therefore $k=-4150$