AlgebraVery hardSolving f(2x) for a linear f
Algebra practice question
The function f is linear, with f(0) = −5 and a slope of 3. For what value of x is f(2x) = 19?
Answer: 4
f(x) = 3x − 5, so f(2x) = 3(2x) − 5 = 6x − 5. Set 6x − 5 = 19: 6x = 24, x = 4.
Common wrong answers
- If you answered 2
- 2 comes from 6x = 12, subtracting 5 instead of adding it to 19.
- If you answered 8
- 8 solves f(x) = 19 (3x − 5 = 19). But the question asks about f(2x), so x is half of that.
- If you answered 24
- 24 is 6x, one step short; divide by 6.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.