If g be the inverse of function f, then $$g(x)=f$$−$$1(x)$$⇒$$f(g(x))=x$$⇒f|(g(x))g$$|$$(x)=1$$⇒g|$$(x)=1f$$|$$(g(x)) also , if $$f($$α$$)=$$β, then $$g($$β$$)=$$αFrom (1), g|$$($$β$$)=1f$$|[$$g($$β$$)$$]∴g|$$($$β$$)=1f$$|$$($$α$$)$$, where $$f($$α$$)=$$βIf f:R→R defined by $$f(x)=x5+e2x$$ and g is the inverse of f , then g|$$(1)=$$

Question

If g be the inverse of function f, then  $$g(x)=f$$−$$1(x)$$⇒$$f(g(x))=x$$⇒f|(g(x))g$$|$$(x)=1$$⇒g|$$(x)=1f$$|$$(g(x)) also , if $$f($$α$$)=$$β, then $$g($$β$$)=$$αFrom (1), g|$$($$β$$)=1f$$|[$$g($$β$$)$$]∴g|$$($$β$$)=1f$$|$$($$α$$)$$, where  $$f($$α$$)=$$βIf  f:R→R defined by $$f(x)=x5+e2x$$ and g is the inverse of f , then g|$$(1)=$$

Infinity Learn · Accepted Answer

$$f(x)=x5+e2xf(0)=0+e0=1f$$|(x)=5$$.$$x4+2$$.$$e2x$$⇒f|$$(0)=5(0)+2(1)=2(gof)(x)=x$$⇒g[$$f(x)]$$=x$$⇒g|$$f(x)$$.f|$$(x)=1$$⇒g|$$f(x)=1f$$|$$(x)put$$  $$x=0$$⇒g|$$(f(0))=1f$$|$$(0)g$$|$$(1)=12$$

Unlock the full solution & master the concept.

Ready to Test Your Skills?

free study material

If g be the inverse of function f, then g(x)=f−1(x)⇒f(g(x))=x⇒f|(g(x))g|(x)=1⇒g|(x)=1f|(g(x)) also , if f(α)=β, then g(β)=αFrom (1), g|(β)=1f|[g(β)]∴g|(β)=1f|(α), where f(α)=βIf f:R→R defined by f(x)=x5+e2x and g is the inverse of f , then g|(1)=

Unlock the full solution & master the concept.

Ready to Test Your Skills?

free study material