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# Function notation — Harder example

Watch Sal work through a harder Function notation problem.

## Want to join the conversation?

• I learnt from this video but the practice questions I solved were completely different from the question solved in the video.
How to solve the questions of function notation related to graph??
• just give the some inputs to given function and take output values then mention them on graph
(1 vote)
• “This is gonna be fun!” cue nervous laughter
• Why wasn't the last answer an option? It looked equivalent to the equation before it was simplified.
• The last answer İSN'T equivalent to the equation before it was simplified.
As you can see at there is a "cube root sign surrounding (x^3+1)" inside another cube root sign outside. İf this inside cube root sign didn't exist around (x^3+1), then you would be right.
At we're raising this "inside cube root of (x^3+1)" to the third power, that's why they cancel each other, and we're left with (x^3+1), add 1 to that and you get the correct answer.
• where can i get more practice on function notation please?
• can't option B also be the answer? it states the exact same thing only in an expanded form.
• On the SAT, you should be careful about parentheses and order of operations in general. Here, notice that in option B) the last +1 is not under the radical, which means that it is different than option C) because you can't combine like terms under an exponent like you maybe could with multiplication.
• am i th eonlyyd alljlfaj
• Bluds brain melted
• Is the SAT practice hard if so scale it one to 20 ?!
• It depends per person based on practice level, familiarity with concepts etc... for me it was a 10-11 (without all the decimals lol)
• Can this answer further be simplified? Can we take x^3 under the radical separately and root 2 separately and then the answer would be x +or- root 2 ?
• Of course not. When there's addition of subtraction inside square roots (or any roots, really), you can't take the root of one value then take the root of another value then add them together.

Meaning:
sqrt(a + b) =/= sqrt(a) + sqrt(b)
sqrt(a - b) =/= sqrt(a) - sqrt(b)

However, when you have multiplication or division, then you can break them into other parts.

sqrt(a * b) = sqrt(a) * sqrt(b)
sqrt(a / b) = sqrt(a) / sqrt(b)

(sqrt is short for square root of, and =/= means "not equal to")
• this is just butter
• Exotic Butters
(1 vote)
• I need help solving u^2 - 125=0
(1 vote)
• Your first step is to look for factors that you can use to solve the equation quickly. Here, I'm not seeing anything, so we'd go to one of the methods for solving quadratic equations that can't be factored: the quadratic formula and completing the square. Completing the square is generally faster when you have just the a and b terms, or if the numbers are easy to work with. I don't really think it'll make much of a difference here, so we'll use the quadratic formula.
x = -b +/- sqrt(b^2 - 4ac) / 2a
x = -0 +/- sqrt(0 - (4)(1)(-125)) / 2(1)
x = +/- sqrt(500) / 2
x = +/- 10/2 * sqrt(5) = +5sqrt(5) and -5sqrt(5)