a(x)=3x-7, b(x)=2-x^3. Find a(b(3))- b(a(x))?

just plug and chug.

b(3) = -25
b(a) = 2-a^3 = 2-(3x-7)^3
so finish it off

Did you know?

Did you know that in algebra, you can use function composition to solve problems like the one given? Function composition involves plugging one function into another. For example, let's take the functions a(x) = 3x-7 and b(x) = 2-x^3. To find a(b(3)), we first substitute 3 into b(x), which gives us b(3) = 2 - 3^3. Simplifying further, we get b(3) = 2 - 27 = -25. Then, we substitute -25 into a(x), resulting in a(-25) = 3(-25) - 7 = -82. Now, to find b(a(x)), we substitute a(x) = 3x-7 into b(x). This yields b(a(x)) = 2 - (3x-7)^3. Expanding and simplifying, we get b(a(x)) = 2 - (27x^3 - 189x^2 + 441x - 343). Combining like terms, the expression becomes b(a(x)) = -27x^3 + 189x^2 - 441x + 345. Ultimately, to calculate a(b(3)) - b(a(x)), we subtract b(a(x)) from a(b(3)). Thus, a(b(3)) - b(a(x)) = -82 - (-27x^3 + 189x^2 - 441x + 345). This expression can be further simplified and solved to obtain the final result. Overall, understanding how to compose functions allows you to solve intricate mathematical problems using a systematic approach.