+0

# Help on this question pls!

0
35
1

Let t(x) = sqrt{3x+1} and f(x)=5-t(x). What is t(f(5))?

Guest Feb 7, 2018

#1
+1720
+1

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, $$t(f(5))=2$$

TheXSquaredFactor  Feb 7, 2018
Sort:

#1
+1720
+1

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, $$t(f(5))=2$$

TheXSquaredFactor  Feb 7, 2018

### 11 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details