Question

f(x)= (-6)squareroot(x+21)

Answer 1

I’m assuming you want basic information about the function f(x) = −6√(x + 21). Here are the key properties and useful items:

- Domain: x ≥ −21 (inside the square root must be nonnegative).
- Range: f(x) ≤ 0, i.e. (−∞, 0]. At x = −21, f(−21) = 0 and as x → ∞, f(x) → −∞.
- x-intercept: (−21, 0). y-intercept: f(0) = −6√21 ≈ −27.495.
- Transformations from y = √x: shift left 21 units, then vertical stretch by factor 6 and reflect across the x-axis.
- Monotonicity: strictly decreasing on its domain.
- Concavity: concave up on its domain (f''(x) > 0 for x > −21).
- Derivative: f'(x) = −3 / √(x + 21) (for x > −21).
- Inverse (swap x and y and solve): f⁻¹(x) = x^2/36 − 21, with domain x ≤ 0 (this recovers the original domain/range swap).

If you want, I can:
- sketch or plot the graph,
- give a table of sample points,
- solve an equation involving f(x),
- or show step-by-step how to get the inverse. Which would you like?