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# Help on this question pls!

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

Feb 7, 2018

#1
+2341
+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, $$t(f(5))=2$$

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Feb 7, 2018

#1
+2341
+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