+2440 By the given information, we know the following:
\(t(x)=\sqrt{3x+1}\\ f(x)=5-t(x)\)
In order to find \(t(f(5))\), we must first evaluate f(x) when x=5:
| \(f(x)=5-t(x)\) | Since t(x) appears in the definition of f(x), plug in t(x) into the f(x) function. |
| \(f(x)=5-\sqrt{3x+1}\) | Now, evaluate f(x) when x=5. |
| \(f(5)=5-\sqrt{3*5+1}\) | Notice how every instance of x has been replaced wth a 5. Now, it is a matter of simplifying. |
| \(f(5)=5-\sqrt{16}\) | |
| \(f(5)=5-4\) | |
| \(f(5)=1\) | |
Now we know that \(t(f(5)=t(1)\) since we just determined that \(f(5)=1\).
| \(t(x)=\sqrt{3x+1}\) | Of course, we want to evaluate when x=1, so replace every instance of x with a 1. |
| \(t(1)=\sqrt{3*1+1}\) | Now, simplify. |
| \(t(1)=\sqrt{3+1}\) | |
| \(t(1)=\sqrt{4}=2\) | |
Therefore, \(t(f(5))=2\)
+2440 By the given information, we know the following:
\(t(x)=\sqrt{3x+1}\\ f(x)=5-t(x)\)
In order to find \(t(f(5))\), we must first evaluate f(x) when x=5:
| \(f(x)=5-t(x)\) | Since t(x) appears in the definition of f(x), plug in t(x) into the f(x) function. |
| \(f(x)=5-\sqrt{3x+1}\) | Now, evaluate f(x) when x=5. |
| \(f(5)=5-\sqrt{3*5+1}\) | Notice how every instance of x has been replaced wth a 5. Now, it is a matter of simplifying. |
| \(f(5)=5-\sqrt{16}\) | |
| \(f(5)=5-4\) | |
| \(f(5)=1\) | |
Now we know that \(t(f(5)=t(1)\) since we just determined that \(f(5)=1\).
| \(t(x)=\sqrt{3x+1}\) | Of course, we want to evaluate when x=1, so replace every instance of x with a 1. |
| \(t(1)=\sqrt{3*1+1}\) | Now, simplify. |
| \(t(1)=\sqrt{3+1}\) | |
| \(t(1)=\sqrt{4}=2\) | |
Therefore, \(t(f(5))=2\)
