Question

Match the operations on the given functions:

𝑓⁡(𝑥) =2⁢𝑥

𝑔⁡(𝑥) =−4⁢𝑥 +5

Drag and drop application.
(𝑓+𝑔)⁡(𝑥)

drop zone empty.
(𝑓−𝑔)⁡(𝑥)

drop zone empty.
(𝑓⋅𝑔)⁡(𝑥)

drop zone empty.
(
𝑓
𝑔

)⁡(𝑥)

drop zone empty.
−6⁢𝑥 +5

−2⁢𝑥 −5

−2⁢𝑥 +5

−8⁢𝑥2 +5

−2+
5
2⁢𝑥

,𝑥≠0

2⁢𝑥
−4⁢𝑥+5

,𝑥≠
5
4

Answer 1

Compute directly:

f(x) = 2x, g(x) = −4x + 5.

- (f + g)(x) = 2x + (−4x + 5) = −2x + 5.
- (f − g)(x) = 2x − (−4x + 5) = 6x − 5.
- (f · g)(x) = 2x(−4x + 5) = −8x^2 + 10x.
- (f/g)(x) = 2x/(−4x + 5), domain: x ≠ 5/4.

(Also useful: (g/f)(x) = (−4x + 5)/(2x) = −2 + 5/(2x), domain: x ≠ 0.)