Answer:
(a) x is a variable, t is a constant
(b)t=-2/5
Explanation:
Given f(x) defined below:
[tex]f(x)=\frac{x+t}{3tx+1}[/tex]
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
[tex]f(3)=-1\implies f(x)=-1,x=3[/tex]
Substitute into f(x) above.
[tex]f(x)=\frac{x+t}{3tx+1}\implies-1=\frac{3+t}{3t(3)+1}[/tex]
Cross multiply
[tex]-1(9t+1)=3+t[/tex]
Distribute the bracket on the left-side.
[tex]\begin{gathered} -9t-1=3+t \\ \text{Collect like terms.} \\ -9t-t=3+1 \\ -10t=4 \\ t=\frac{4}{-10} \\ t=-\frac{2}{5} \end{gathered}[/tex]
The value of t when f(3)=-1 is -2/5.
