Functions;;

Let f:X â†’Y be a function defined by f(x) = asin(x+Ï€/4)+bcosx +c. If c is both one-one and onto, find the sets X and Y

4 Answers

arrange the given eq. as--
a√2 sinx + (a√2+b )cosx +c

this equation is of form a sin\phi + b cos\phi +c.....

min. value of this expression is - √a²+b²+c
and maximum value is + √a²+b²+c

now u can apply this on the original question to find Y and then X

in the above, dont confuse both the a's and b's .. they are the same in symbol but different...

in the above, dont confuse both the a's and b's .. they are the same in symbol but different...

what is meant by 'c is both one one and onto'? is it a function?

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω