Question

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Answer 1

Răspuns:

Explicație pas cu pas:

1) f:D --> R ; f(x) = 1-5x

f(-4) = 1-5·(-4) = 1+20 = 21

f(4) = 1-5·4 = 1-20 = -19 =>

f(-4) > f(4)

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2) f: D --> R ; f(x) = 2x+3

f⁻¹(f(x)) = x <=> f⁻¹(y) = x =>

y = 2x+3 => 2x = y-3 => x = (y-3)/2 =>

f⁻¹(x) = (x-3)/2

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3) f: D --> R ; f(x) =(2-x)/4 +3 ; f(x) ≤ 0 =>

(2-x)/4 + 3 ≤ 0 <=>

(2-x+12)/4 ≤ 0 <=> (14-x)/4 ≤ 0 =>

14-x ≤ 0 => x ≥ 14 =>

x ∈ [14 ; +∞)

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4) f: D --> R ; f(x) = 5-11x

a) f(x) = 0 => 5-11x = 0 =>

5 = 11x => x = 5/11

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b)

      x I -∞         5/11       +∞

5-11x  I +++++++0------------

f(x) = strict descrescatoare

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c) unghiul dintre f(x) si Ox este un unghi obtuz

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5) Ix-1I = 3 =>

x-1 = 3 => x = 4

-x+1 = 3 => x = -2

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6) mx = 3(x-m)+3 =>

mx = 3x-3m+3 =>

mx-3x = 3-3m =>

x(m-3) = 3(1-m) =>

x = 3(1-m)/(m-3)