Question

For the function f (x)=6/2x-3, find the value of each expression below
$f(x) = \frac{6}{2x - 3}$
a. f (1)
b. f (0)
c. f (-3)
d. f (1.5)
e. what value of x would make f(x)=4 ?

Answer 1

we are given

$f(x) = \frac{6}{2x - 3}$

(a)

For finding f(1), we can plug x=1 into f(x)

we get

$f(1) = \frac{6}{2*1 - 3}$

$f(1) = -6$...........Answer

(b)

For finding f(0), we can plug x=0 into f(x)

we get

$f(0) = \frac{6}{2*0 - 3}$

$f(0) = -2$...........Answer

(c)

For finding f(-3), we can plug x=-3 into f(x)

we get

$f(-3) = \frac{6}{2*-3 - 3}$

$f(-3) = -\frac{2}{3}$...........Answer

(d)

For finding f(1.5), we can plug x=1.5 into f(x)

we get

$f(1.5) = \frac{6}{2*1.5 - 3}$

$f(1.5) =\infty$...........Answer

(e)

We can set f(x)=4

and then we can solve for x

$f(x) = \frac{6}{2x - 3}=4$

$\frac{6}{2x-3}\left(2x-3\right)=4\left(2x-3\right)$

$\frac{4\left(2x-3\right)}{4}=\frac{6}{4}$

$2x-3=\frac{3}{2}$

$2x=\frac{9}{2}  $

$x=\frac{9}{4}  $...............Answer