Question

a. Is X a variable or a constant? Is t a variable or a constant? b. If f(3) = -1, find all possible values of t.

Answer 1

(a) x is a variable, t is a constant

(b)t=-2/5

Explanation:

Given f(x) defined below:

`f(x)=(x+t)/(3tx+1)`

Part A

The value of x can take on any value, which means, it varies.

• Thus, x is a variable.

Since the function, f(x) is a function of x, t is a constant.

Part B

If f(3)=-1

`f(3)=-1\implies f(x)=-1,x=3`

Substitute into f(x) above.

`f(x)=(x+t)/(3tx+1)\implies-1=(3+t)/(3t(3)+1)`

Cross multiply

`-1(9t+1)=3+t`

Distribute the bracket on the left-side.

`\begin{gathered} -9t-1=3+t \\ \text{Collect like terms.} \\ -9t-t=3+1 \\ -10t=4 \\ t=(4)/(-10) \\ t=-(2)/(5) \end{gathered}`

The value of t when f(3)=-1 is -2/5.