Tutor profile: Elena C.
Subject: Linear Algebra
Find the domain of the following: f(x)=3/(x-6)
Domain is the complete set of functions that are possible for this equation; you cannot divide by zero. Step 1: ask yourself, how can I ensure I will not divide by zero? Answer is to look at the denominator: (x-6) Step 2: set the denominator to 0 to solve for x; this will make it so we can find what value of x makes the denominator 0. x-6=0 Step 3: solve for x: x-6=0 therefore, x=6 Step 4: write the set(s) of the domain. (-infinity, 6)U(6,infinity); this is saying that any negative number to 6 and 6 to any number can be solved for in the function. The only number that will not make the function possible is 6
Solve and simplify for k: -4k+12=--2k-8
We know that k by itself needs to be on the left side and everything else on the right Step 1: move 2k to the left; to do this subtract 2k from -4k+12: -4k+12-(-2k) - since -4k and -2k have the same factor of k, we can add them together to simplify the equation. -4k-(-2k)=-4k+2k= -2k Step 2: so far out equation is -2k+12=-8; now we need to move 12 to the right side, to do this we need to subtract 12 to the right side. -8-12 = -20 Step 3: now we have the following equation from Step 1 and Step 2: -2k=-20; we are still looking for k by itself. since -2k is really -2*k, to have k by itself we need to divide by -2 from both sides. -2k/-2=-20/-2 Step 4: simplify both sides of the equation: -2k/-2 reduces to k and -20/-2 reduces to 10 for a final equation of k=10 Ensure your negatives are correct and double check your work. Step 5: check your solution by replacing k=10 into the original equation: (-4*10)+12=(-2*10)-8; -40+12= -20-8; -28= -28; since both sides of the equation are equal, the solution found in steps 1-4 are correct.
Factor and then solve: f(4): x^2-15x+56
Step 1: ask how many equations we need; since the largest factor of x is x^2, we will need 2 equations Step 2: ask yourself, are the two equations going to be positive, negative, or one of each? Since the first sign is negative and the second is positive, we will have two negative equations Step 3: set up the equations; (x - _ )(x- _ ) Step 4a: Figure out what goes in the blanks; look at the single number, 56. The ask what sets of numbers when multiplied together make up 56? 1x56, 2x28, 7x8 Step 4b: From the set of numbers in 4a, which two can be added or subtracted together to make 15; this will help find 15x - the answer is 7 and 8; 7+8=15 Step 5: Put the set of numbers from 4b into step 3; since both equations are x minus, order does not matter... so our final answer is (x-7)(x-8) Step 6: Double check your work. multiple the two equations. (x*x)+(a*-8)+(-7*x)+(-7*-8)=x62-15x+56 Step 7: solve for f(4) - replace 4 into x. (4-7)(4-8) = -3*-4=12 Step 8: check your work and replace 4 with original equation: 4^2-(15*4)+56=16-60+56=12 Since Step 7 and Step 8 match we know we did the problem correctly
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